Does Blender have a tool similar to Smooth Boundary in Meshmixer?
Yes. You can use either the smooth function (search it in the program, or use it from the toolshelf), or, for more control, use proportional editing. The latter even comes with a few falloff setups to choose from!

Please Take Notice: The latter is really intended more for if you're physically editing the mesh in some manner, but with a strong enough effect radius, the actual movement requirement can be minuscule.